Question

Problems Set at an Oral Examination.
Show that every odd number can be represented as a difference of the squares of two integers.

Answer 1

Any odd number can be written in the form of $p=2n+1$.

Now, $2n+1=(n+1{)}^2-n^2$

$⟹p=(n+1{)}^2-n^2$

Hence, every odd number can be written as the difference of the squares of two integers.